Calculus 2 Quiz
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SEQUENCES & SERIES
Question 1
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Let
S
p
=
∑
n
=
1
∞
(
−
1
)
n
−
1
n
p
S_p = \sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n^p}
S
p
=
∑
n
=
1
∞
n
p
(
−
1
)
n
−
1
. Which of the following statements is true?
A
S
p
S_p
S
p
converges absolutely for
p
>
1
p > 1
p
>
1
and conditionally for
0
<
p
≤
1
0 < p \le 1
0
<
p
≤
1
.
B
S
p
S_p
S
p
converges conditionally for
p
>
1
p > 1
p
>
1
and absolutely for
0
<
p
≤
1
0 < p \le 1
0
<
p
≤
1
.
C
S
p
S_p
S
p
converges conditionally for all
p
>
0
p > 0
p
>
0
.
D
S
p
S_p
S
p
converges absolutely for all
p
>
0
p > 0
p
>
0
.
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